Some patients with this disease receive enzyme replacement therapy with weekly injections of the drug PEG-ADA (ADAGEN). This drug may increase the number of immune cells and reduce infections, but it is not a cure. Gene transfer therapy, in which a normal ADA gene is inserted into the patient s cells, attempts to correct the underlying cause of disease. This therapy has been tried in a small number of patients with varying degrees of success. In this study, the gene will be inserted into the patient s stem cells (cells produced by the bone marrow that mature into the different blood components white cells, red cells and platelets).